On description of impulsive noise removal using PWL filter model

The classical method for impulsive noise removal in image signals consists of two steps, i.e., a step for impulse detection and a step for estimation of the pixels corrupted by impulsive noise. In this paper, we show that the step of impulse detection can be described very suitably by piecewise-linear (PWL) functions which explain intuitively the process of detection as a partition of the signal domain space. A PWL filter model is then proposed. In such a filter model, we can use either a linear or a nonlinear subfilter to estimate the corrupted pixels. For the latter, using a median subfilter yields a multi-level PWL filter. The filter model is simulated and its excellent result is compared to that of a median filter.